應(yīng)yl7703永利官網(wǎng)王智誠教授和孫建文副教授的邀請(qǐng)，南開大學(xué)馬世旺教授將于2022年12月14日-12月15日與我校有關(guān)師生進(jìn)行在線學(xué)術(shù)研討，其中12月15日舉行線上專題學(xué)術(shù)報(bào)告。
報(bào)告題目: Existence and asymptotic behavior of normalized solutions for Choquard type equations
時(shí) 間：12月15日9:00.
騰訊會(huì)議ID：384-411-384
報(bào)告摘要：In this talk, we prensent some resent results on the existence and multiplicity of normalized solutions of the nonlinear Choquard equation$$-\Delta u+\lambda u=(I_\alpha \ast F(u))F’(u), \quad {\rm in} \ \mathbb R^N, \eqno(Ch) $$ under the normalization constraint $\int_{\mathbb R^N}|u|^2=c^2$, where $N\ge 3$ is an integer, $I_\alpha$ is the Riesz potential and the frequency $\lambda\in \mathbb R$ appears as a Lagrange multiplier. For a class of Choquard type equations with combined nonlinearities, we first fix the frequency $\lambda$ and study the asymptotic behavior of positive ground state solutions $u_\lambda$ as $\lambda \to 0$ (resp. $\lambda \to \infty$). We prove that after {\em a suitable rescaling} the ground state solutions $u_\lambda$ converge in $H^1(\mathbb R^N)$ to a particular solution of some limit equations. We also establish a sharp asymptotic characterisation of such a rescaling, an optimal uniform decay estimates of ground states $u_\lambda$ and the exact asymptotic expression of $\|u_\lambda\|_2^2$. Applying the above conclusions to the associated mass constrained problem with normalization constraint $\int_{\mathbb R^N}|u|^2=c^2$, we obtain the existence, multiplicity and exact asymptotic behavior of positive normalized solutions of such a problem as $c\to 0$ and $c\to \infty$.
歡迎廣大師生光臨!
馬世旺教授簡介
馬世旺，南開大學(xué)數(shù)學(xué)學(xué)院教授、博士生導(dǎo)師。1997年于湖南大學(xué)獲理學(xué)博士學(xué)位，先后工作于上海交通大學(xué)、南開大學(xué)。已主持完成國家自然科學(xué)基金項(xiàng)目5項(xiàng)、高等學(xué)校博士學(xué)科點(diǎn)專項(xiàng)科研基金項(xiàng)目1項(xiàng)。研究領(lǐng)域?yàn)榉蔷€性分析、微分方程與動(dòng)力系統(tǒng)，在J. Differential Equations、CVPDE、 J. Dynam. Differential Equations，中國科學(xué)等國內(nèi)外權(quán)威數(shù)學(xué)期刊發(fā)表學(xué)術(shù)論文90余篇，數(shù)學(xué)評(píng)論顯示，研究成果已被引用1000多次，單篇引用超過200次。
甘肅應(yīng)用數(shù)學(xué)中心
甘肅省高校應(yīng)用數(shù)學(xué)與復(fù)雜系統(tǒng)省級(jí)重點(diǎn)實(shí)驗(yàn)室
yl7703永利官網(wǎng)
萃英學(xué)院
2022年12月9日
